%I #11 Dec 29 2014 18:10:51

%S 1,1,9,36,84,126,126,84,36,9,1,81,2916,61236,826686,7440174,44641044,

%T 172186884,387420489,387420489,13947137604,223154201664,2082772548864,

%U 12496635293184,49986541172736,133297443127296,228509902503936,228509902503936,101559956668416

%N Number of shapes of balanced 9-ary trees with n nodes, where a tree is balanced if the total number of nodes in subtrees corresponding to the branches of any node differ by at most one.

%C a(n) = 1 for n in { A002452 }.

%H Alois P. Heinz, <a href="/A229394/b229394.txt">Table of n, a(n) for n = 0..820</a>

%p a:= proc(n) option remember; local m, r; if n<2 then 1 else

%p r:= iquo(n-1, 9, 'm'); binomial(9, m) *a(r+1)^m *a(r)^(9-m) fi

%p end:

%p seq(a(n), n=0..91);

%Y Column k=9 of A221857.

%Y Cf. A175673.

%K nonn,look

%O 0,3

%A _Alois P. Heinz_, Sep 21 2013